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Study on linear elastic fracture mechanics PDF

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Running head: STUDY ON LINEAR ELASTIC FRACTURE MECHANICS
LINEAR ELASTIC FRACTURE MECHANICS: DEVELOPMENT AND ADVANCEMENT
IN STUDY OF CATASTROPHICS FAILURES & FRACTURE ANALYSIS
Name of the student:
Name of the university:
Author note:
STUDY ON LINEAR ELASTIC FRACTURE MECHANICS1
Table of Contents
Introduction:....................................................................................................................................2
Related theories:..............................................................................................................................3
Formulas and assumptions used in LEFM:.................................................................................3
Advantages and drawbacks..........................................................................................................4
Gradual development in this field:..................................................................................................5
Recent research work:......................................................................................................................6
LEFM Characterization of an Anisotropic Shale:.......................................................................6
Conclusion:......................................................................................................................................8
References:......................................................................................................................................9
STUDY ON LINEAR ELASTIC FRACTURE MECHANICS2
Introduction:
Fracture is one of the most serious problems that the society has been facing from a very
long time. Fractures have started occurring ever since the inception of manmade structures in the
history of the world. The problem now is even worse than what is used to be centuries back since
more and more technologies and advancement in manmade structures are coming up with
increased complexities. Much research has been carried out in the past, which has only
generalized the preexisting technologies. However not much research has been done on the
specific trends of elastic fractures.
This topic is extremely important to be further researched on. Different recommendations
as well as feedbacks regarding minimizing catastrophic accidents in the future can be obtained.
The different kinds of micro mechanisms that leads to the fracture failures can be understood
with an in depth analysis of this topic (Kanget al.2015). The roles of “process zone” as well as
the two dimensions of the fracture phenomena, which are deterministic and the probabilistic
dimensions, can be addressed.
Linear Elastic Fracture Mechanics or LEFM assumes the material to beisotropic as well
as linear elastic in nature and based on this assumption, the field of stress by the side of the crack
tip can be calculated using the elasticity theory. When the stresses in the crack tip area exceeds
the toughness of the material fracture, the crack grows (Minhajuddin, Saha and Biligiri 2015).
Most of the formulas are derived either for eitherplane stressorfor plane strains, which are
associated with three loading modes of loadings on a body that is cracked:opening,sliding, as
well astearing.
STUDY ON LINEAR ELASTIC FRACTURE MECHANICS3
Related theories:
Formulas and assumptions used in LEFM:
The basic analysis of LEFM is the stress in the area of the cracked tip. It is the location
function, the conditions of loading conditions as well as the specimen geometry, which can be
shown using the formula as shown below in the diagram. It is assumed that there is no stress
intensity factor in the idea scenario.
Figure 1: Basic analysis formula for LEFM(Wanhill, Molent and Barter 2013).
However, in practice the stress intensity factor or “K” is calculated based on the crack tip
stress and it is compared against the fracture toughness as a function of the location, loading as
well as the geometry. The location is represented asrandis the coordinate system.
Figure 2: Calculation of stress intensity factor “k” in LEFM(Weißgraeberet al.2016).
The fracture toughness can be calculated using a material specific stress intensity factor
Kc(Nejati, Paluszny and Zimmerman 2015). It is assumed that the stress intensity factororKis
lesser thanKc.
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